Gray Code
This is a variable weighted code and is cyclic. This means that it is arranged so that every transition from one value to the next value involves only one bit change.
The gray code is sometimes referred to as reflected binary, because the first eight values compare with those of the last 8 values, but in reverse order.

Decimal

Binary

Gray

0

0000

0000

1

0001

0001

2

0010

0011

3

0011

0010

4

0100

0110

5

0101

0111

6

0110

0101

7

0111

0100

8

1000

1100

9

1001

1101

10

1010

1111

11

1011

1110

12

1100

1010

13

1101

1011

14

1110

1001

15

1111

1000

The gray code is often used in mechanical applications such as shaft encoders.
Modulo 2 Arithmetic
This is binary addition with the carry ignored.
Converting Gray Code to BinaryA. write down the number in gray code B.
the most significant bit of the binary number is the most significant bit of the gray code C.
add (using modulo 2) the next significant bit of the binary number to the next significant bit of the gray coded number to obtain the next binary bit D.
repeat step C till all bits of the gray coded number have been added modulo 2
the resultant number is the binary equivalent of the gray number

Converting Binary to GrayA.
write down the number in binary code B.
the most significant bit of the gray number is the most significant bit of the binary code C.
add (using modulo 2) the next significant bit of the binary number to the next significant bit of the binary number to obtain the next gray coded bit D.
repeat step C till all bits of the binary coded number have been added modulo 2
the resultant number is the gray coded equivalent of the binary number

The answer is 1101101Excess 3 Gray Code
In many applications, it is desirable to have a code that is BCD as well as unit distance. A unit distance code derives its name from the fact that there is only one bit change between two consecutive numbers. The excess 3 gray code is such a code, the values for zero and nine differ in only 1 bit, and so do all values for successive numbers.
Outputs from linear devices or angular encoders may be coded in excess 3 gray code to obtain multi-digit BCD numbers.